The lattice relaxation around Ga in CdTe is investigated by means of extended X-ray absorption spectroscopy (EXAFS) and density functional theory (DFT) calculations using the linear augmented plane waves plus local orbitals (LAPW+lo) method. In addition to the substitutional position, the calculations are performed for DX- and A-centers of Ga in CdTe. The results of the calculations are in good agreement with the experimental data, as obtained from EXAFS and X-ray absorption near-edge structure (XANES). They allow the experimental identification of several defect structures in CdTe. In particular, direct experimental evidence for the existence of DX-centers in CdTe is provided, and for the first time the local bond lengths of this defect are measured directly.7th International Workshop on X-Ray Damage to Biological Crystalline Samples, Mar 14-16, 2012, Englan